How many 4-digit numbers can be formed using | vedclass

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Question

(A) To form a $4$-digit number using the digits $1, 2, 3, 4, 5, 6, 7$ without repetition,we need to select $4$ digits out of $7$ and arrange them.
Th

Vedclass · Accepted Answer

$840$

Vedclass · Answer

(A) To form a $4$-digit number using the digits $1, 2, 3, 4, 5, 6, 7$ without repetition,we need to select $4$ digits out of $7$ and arrange them.
The number of ways to select and arrange $4$ digits out of $7$ is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.
Here,$n = 7$ and $r = 4$.
Number of ways = $^7P_4 = \frac{7!}{(7-4)!} = \frac{7!}{3!} = 7 	imes 6 	imes 5 	imes 4 = 840$.
Note: The original provided option $480$ is incorrect based on the standard permutation calculation for $4$ distinct digits from $7$.

How many $4$-digit numbers can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ such that each digit is used only once?

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